Because it is known that the resistance of a conductor
is directly proportional to its length, and if we are
given the resistance of the unit length of wire, we can
readily calculate the resistance of any length of wire of
that particular material having the same diameter. Also,
because it is known that the resistance of a conductor
is inversely proportional to its cross-sectional area, and
if we are given the resistance of a length of wire with
unit cross-sectional area, we can calculate the resistance
of a similar length of wire of the same material
with any cross-sectional area. Therefore, if we know
the resistance of a given conductor, we can calculate
the resistance for any conductor of the same material
at the same temperature. From the relationship:

R = (ρ × l)/A

It can also be written:

R1/R2 = l1/l2 = A1/A2

While the System International (SI) units are commonly
used in the analysis of electric circuits, electrical
conductors in North America are still being manufactured
using the foot as the unit length and the mil (one
thousandth of an inch) as the unit of diameter. Before
using the equation R = (ρ × l)/A to calculate the resistance
of a conductor of a given AWG size, the crosssectional
area in square meters must be determined
using the conversion factor 1 mil = 0.0254 mm. The
most convenient unit of wire length is the foot. Using
these standards, the unit of size is the mil-foot. Thus,
a wire has unit size if it has a diameter of 1 mil and
length of 1 foot.

In the case of using copper conductors, we are spared
the task of tedious calculations by using a table as
shown in Figure 10-42.

Note that cross-sectional
dimensions listed on the table are such that each
decrease of one gauge number equals a 25 percent
increase in the cross-sectional area. Because of this,
a decrease of three gauge numbers represents an
increase in cross-sectional area of approximately a 2:1
increase. Likewise, change of ten wire gauge numbers
represents a 10:1 change in cross-sectional area — also,
by doubling the cross-sectional area of the conductor,
the resistance is cut in half. A decrease of three wire
gauge numbers cuts the resistance of the conductor of
a given length in half.